IEEE Trans Neural Netw Learn Syst. 2014 Mar;25(3):483-94. doi: 10.1109/TNNLS.2013.2275959.
This paper presents the design of a complex-valued differential neural network identifier for uncertain nonlinear systems defined in the complex domain. This design includes the construction of an adaptive algorithm to adjust the parameters included in the identifier. The algorithm is obtained based on a special class of controlled Lyapunov functions. The quality of the identification process is characterized using the practical stability framework. Indeed, the region where the identification error converges is derived by the same Lyapunov method. This zone is defined by the power of uncertainties and perturbations affecting the complex-valued uncertain dynamics. Moreover, this convergence zone is reduced to its lowest possible value using ideas related to the so-called ellipsoid methodology. Two simple but informative numerical examples are developed to show how the identifier proposed in this paper can be used to approximate uncertain nonlinear systems valued in the complex domain.
本文提出了一种用于复数域中定义的不确定非线性系统的复值微分神经网络标识符的设计。该设计包括构建一个自适应算法来调整标识符中包含的参数。该算法是基于一类特殊的受控李雅普诺夫函数获得的。使用实用稳定性框架来描述识别过程的质量。实际上，通过相同的李雅普诺夫方法推导出识别误差收敛的区域。该区域由影响复数值不确定动态的不确定性和扰动的幂来定义。此外，使用与所谓的椭球方法相关的思想，将该收敛区域缩小到尽可能低的值。开发了两个简单但信息丰富的数值示例，以展示本文提出的标识符如何用于逼近复数域中的不确定非线性系统。
